Abstract
For each interval I in IR = (−∞, ∞) let B(I) denote the σ-field of Borel subsets of I. For each t ∈ IR + = [0, ∞), let B t denote B([0, t]) and let B denote \(B(I{R_ + }) = {V_{t \in I{R_ + }}}\) B t — the smallest σ-field containing B t for all t in IR+. Let \(overline {I{R_ + }} = [0,\infty ]\) and \(overline B\) denote the Borel σ-field of \(overline {I{R_ + }}\) generated by B and the singleton {∞}. Let λ denote the Lebesgue measure on IR.
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© 1990 Birkhäuser Boston
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Chung, K.L., Williams, R.J. (1990). Preliminaries. In: Introduction to Stochastic Integration. Probability and Its Applications. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4480-6_1
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DOI: https://doi.org/10.1007/978-1-4612-4480-6_1
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8837-4
Online ISBN: 978-1-4612-4480-6
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